Performance of the Quasar Spectral Templates for the Dark Energy Spectroscopic Instrument

We select spectra from SDSS DR16 using attributes from the DR16 QSO catalog (Lyke et al. 2020). The spectra were collected with the Sloan telescope (Gunn et al. 2006) using the (e)BOSS spectrographs (Smee et al. 2013). QSO targets in this analysis were selected as described in Ross et al. (2012) and Myers et al. (2015).

We use QSO spectra with a Z_PCA redshift of 0.05 ≤ z ≤ 5.0 and ZWARN_PCA = 0 to develop the new QSO templates. The method for estimating Z_PCA is explained in Section 4.4 of Lyke et al. (2020). Pixels in SDSS spectra are binned on a logarithmic wavelength array with constant spacing. The average signal-to-noise ratio (S/N) per pixel of each spectrum is determined over all pixels with a RF wavelength of λ_RF > 1216 Å, after excluding pixels flagged as having poor sky subtraction. We also exclude pixels at wavelengths shorter than 1216 Å from the S/N measurement, as Lyα absorption features dominate the spectrum at these wavelengths. Spectra with an average S/N per pixel > 5 are included in the training sample. The final selection provides 207,956 unique spectra.

We reduce the impact of nonintrinsic foreground features in the spectra by applying various corrections. The corrections applied are identical to those in BD22 except with changes to filtering outlier pixels. We first correct for galactic extinction using the dust map of Schlegel et al. (1998) and extinction law of Fitzpatrick (1999). We then mask pixels flagged for poor sky subtraction and those that deviate negatively by more than 2σ from the ratio of the measured flux to the flux smoothed by a 30 pixel median filter (corresponding to approximately 2000 km s⁻¹). The latter mask aims to remove contamination from foreground IGM absorption but may unintentionally mask some intrinsic absorption features, such as narrow BALs. Lastly, each spectrum is shifted to its RF solution.

DESI is installed on the Mayall Telescope at Kitt Peak National Observatory. The focal plane holds 5000 optical fibers, steered by robotic positioners to the locations of survey targets (Myers et al. 2023; Silber et al. 2023). The focal plane is split into 10 wedges, called petals, each holding 500 fibers that direct light to a multiobject fiber spectrograph. A single pointing of the 10 petals is collectively referred to as a tile. A complete description of DESI instrumentation is provided in Abareshi et al. (2022).

Spectra collected by DESI are processed in a fully automatic pipeline (Guy et al. 2023) and then classified by Redrock and the QSO afterburners. The spectra are binned on a wavelength array with constant linear spacing between pixels.

We use five samples of DESI spectra for validating the new QSO templates, detailed in the following paragraphs: the DESI Truth Table, QSO Main, Survey Validation (SV) Repeat Exposures, the One-Percent Survey, and the Guadalupe Internal Data Assembly (hereafter Guadalupe). All spectra were classified with Redrock version 0.15.4 and the QSO afterburners using the previous QSO templates. The SV and One-Percent spectra and corresponding catalogs with these classifications will be publicly available in the EDR. The Guadalupe data used in this work will be released as part of DESI Year 1 and will use classifications from the QSO templates presented in this paper.

DESI Truth Table. The first validation sample is selected from the SV program and consists of spectra from eight tiles: 80605, 80606, 80607, 80608, 80609, 80610, 80613, and 80742. These tiles were exposed multiple times to achieve a higher cumulative effective exposure depth than the nominal main survey. Coadding all the spectra obtained for a target enabled reliable VI of early survey data to assess pipeline performance and preliminary target selection methods (Allende Prieto et al. 2020; Raichoor et al. 2020; Ruiz-Macias et al. 2020; Yèche et al. 2020; Zhou et al. 2020). As a result, there exist VI labels for many of these spectra that include a spectral class, redshift, and confidence in the visual assessment. Confidence is provided on a scale of 0–4, with 0 indicating no signal and 4 indicating two or more secure spectral features are identifiable. A VI confidence of equal to or greater than 2.5, meaning at least one inspector indicated a probable classification with at least one clear spectral feature or several weak features, is treated as truth (see Alexander et al. 2023; Lan et al.2023, for details).

We use the truth labels to determine the classification accuracy and sample completeness with the new QSO templates for the resulting QSO and galaxy samples (Section 4.1). In total, we test performance on 17,397 cumulative spectra with confident VI labels. The breakdown of spectral classes assigned from VI in the DESI Truth Table is given Table 1.

QSO Main. The QSO target selection for SV includes objects fainter than the main survey (Chaussidon et al. 2023). We study performance on main survey QSO targets by restricting the DESI Truth Table to target type "QSO" and r < 23. This subsample contains 2632 cumulative spectra, of which a nonnegligible fraction is non-QSOs according to VI. The VI spectral-class distribution within QSO Main is included in Table 1.

SV Repeat Exposures. The individual exposures of targets in the DESI Truth Table tiles and six additional deep tiles (80620, 80678, 80690, 80695, 80699, and 80711) were randomly sampled to create several spectra of each target equivalent to exposures at the main survey depth. We use the spectra of QSO targets in this sample to quantify the redshift precision by comparing the redshift estimates for different spectra of the same target (Section 4.2.1).

One-Percent Survey and Guadalupe. The One-Percent Survey, occasionally referred to as SV3 (Chaussidon et al. 2023), was collected primarily between 2021 April 5 and 2021 May 13, using exposure times 20% longer than the fiducial. Guadalupe is the first two months of main survey data collected by DESI between 2021 May 14 and July 9. We use these last two samples for measuring the bias on QSO redshifts and for additional testing of QSO redshift precision (Section 4.2.2). We also use Guadalupe to check the spectra of targets that change classification with the change of QSO templates (Section 4.1.3), evaluating the overall accuracy of the changes and determining any new potential failure modes.

We use the clustering technique of BD22 to compress the training sample of QSO spectra into groups that exhibit low internal diversity. The clustering method is based on SetCoverPy, ³⁶ an archetype technique developed by Zhu (2016). The only free parameter in the clustering method is the reduced χ² threshold (Equation (1) in BD22), below which two spectra are considered similar and therefore belong to the same cluster. This parameter is tuned to maximize the similarity of spectra in the same cluster without creating excessive outliers (i.e., spectra not within the ${\chi }_{\mathrm{red}}^{2}$ threshold to any other spectrum). We refer to Section 3 of BD22 for a full description of the clustering technique and outlier identification. We only provide a brief overview, focusing on details specific to this work.

We use the ${\chi }_{\mathrm{red}}^{2}$ distance metric from BD22 to measure the similarity between all pairs of spectra within a clustering bin (bins are described in the following paragraphs). The ${\chi }_{\mathrm{red}}^{2}$ metric includes a two-parameter term (c λ^Δα ) that is applied to the higher S/N spectrum of each pair to account for the difference in broadband continua between the spectra. The values of c and Δα are determined for each pair so that the ${\chi }_{\mathrm{red}}^{2}$ is minimized. QSO continua are well described by a single power law between the Lyα and Hβ emission lines (e.g., Brotherton et al. 2001; Vanden Berk et al. 2001), permitting this term to be reasonably applied to QSO pairs at z > 1. The term's validity breaks at lower redshifts as wavelengths longer than that of the Hβ line enter the spectral coverage. We therefore split the training sample into two overlapping subsamples for clustering: ³⁷ 1.0 < z < 2.6 and z < 1.3. For the z < 1.3 subsample, c = 1 and Δα = 0 in all ${\chi }_{\mathrm{red}}^{2}$ calculations. Spectra with redshifts above z = 2.6 are excluded from initial clustering and incorporated into clusters at a subsequent stage, as described later in this section.

The training subsamples are binned on discrete intervals of Δz ≈ 0.15–0.35 to account for redshift evolution of spectral features, described in Table 2. Within each redshift bin, the spectra are cropped to the overlapping wavelength range defined by the shortest wavelength of the lowest-redshift spectrum and the longest wavelength of the highest-redshift spectrum in the bin. Additionally, pixels with an RF wavelength shorter than 1216 Å are masked to avoid the spurious signal from the Lyα forest. The spectra are then normalized according to the median flux density measured over the common RF wavelength range. The pixel diversity mask (Section 3.2.1 in BD22) is applied at this stage. This mask focuses spectral comparisons on the top 32% of pixels exhibiting the most flux variation within a given redshift bin to maximize the information content in the resulting clusters.

Table 2. The Number of QSOs in Each Redshift Bin, the Median S/N of Spectra in the Bin, and RF Wavelength Range Used for Clustering

					High S/N			Low S/N
Redshift	QSOs	Median	${\lambda }_{\min }$	${\lambda }_{\max }$	Initial ${\chi }_{\mathrm{red}}^{2}$	Clusters	Outliers	Initial ${\chi }_{\mathrm{red}}^{2}$	Clusters	Outliers
		S/N	(Å)	(Å)
0.0 < z < 0.35	3289	⋯	3611	7687	2.477	138	259	⋯	⋯	⋯
0.35 < z < 0.7	15,847	7.89	2674	6104	1.320	451	305	1.053	464	228
0.7 < z < 0.85	11,541	7.45	2124	5617	1.241	362	140	1.067	390	82
0.85 < z < 1.0	12,125	7.47	1952	5189	1.100	411	102	0.989	392	55
1.0 < z < 1.15	12,218	7.49	1805	4818	1.034	335	43	0.950	296	29
1.15 < z < 1.3	13,048	7.42	1679	4519	1.016	337	58	0.950	330	51
1.0 < z < 1.2	16,463	7.47	1805	4724	1.083	472	66	0.950	496	61
1.2 < z < 1.4	18,117	7.43	1641	4332	1.080	445	83	0.952	489	57
1.4 < z < 1.6	17,992	7.34	1505	3999	1.149	480	167	1.017	527	83
1.6 < z < 1.8	16,918	7.36	1389	3714	1.266	432	300	1.083	473	109
1.8 < z < 2.0	17,310	7.76	1289	3460	1.376	398	510	1.123	438	154
2.0 < z < 2.2	17,145	7.71	1203	3249	1.609	369	569	1.255	399	242
2.2 < z < 2.4	20,155	7.60	1128	3058	1.899	435	670	1.441	531	296
2.4 < z < 2.6	14,796	7.60	1062	2889	2.077	330	602	1.516	423	344
2.6 < z < 5.0	26,258	⋯	⋯	⋯	⋯	⋯	616	⋯	⋯	464

Note. The median S/N is used to split the redshift bin into two evenly sized subbins in which clustering is performed independently. The final number of clusters and outliers are reported after the outlier retrieval stage. The lowest-redshift bin is not split on S/N owing to small numbers and the results are for the full bin. A different clustering method is used for the highest-redshift bin, described in the text.

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Each redshift bin is further binned on its median S/N, excluding the lowest-redshift bin owing to low numbers. Our motivation for subbinning on S/N is twofold. First, the noise levels vary greatly across the sample and splitting on S/N allows us to tune the threshold distance for clustering to achieve a meaningful measure of similarity between spectra, given their noise levels. Second, many spectral features are known to evolve with luminosity (e.g., Shields 2007; Jensen et al. 2016). We can treat S/N as a loose proxy for luminosity since the QSOs are at the same approximate redshift and SDSS exposure times are relatively consistent.

Clustering is performed independently in the high-S/N and low-S/N bins of each redshift bin. We enforce ${\chi }_{\mathrm{red}}^{2}\geqslant 0.95$ when determining the initial clustering threshold distances. The same outlier retrieval method in BD22 is applied to the resulting clusters to maximize diversity coverage. The initial threshold ${\chi }_{\mathrm{red}}^{2}$ and final clustering results are summarized in Table 2.

The clustering technique produces 11,043 nonexclusive clusters of similar spectra and 6388 unique outliers. The cluster sizes range from two spectra to several hundred spectra. The smaller clusters often contain more peculiar QSOs such as BALQSOs, dust-reddened QSOs, systems with extremely shifted lines, or QSOs with unusually high equivalent widths, while larger clusters contain more typical QSO spectra displaying blue continua. Though the degree of overlap between clusters varies greatly, larger clusters tend to share more spectra with other larger clusters than smaller clusters do in general. To first order, the collection of the clusters represents the range of spectral diversity observed across the full training sample. Many spectra identified as outliers in clustering exhibit calibration or classification errors, peculiar features such as BALs or atypical emission line strengths or ratios, or have incorrect redshifts from Z_PCA, as determined from VI. The natural segregation of these spectra facilitate contaminant rejection before training the final spectral model (See Section 3.2).

The ${\chi }_{\mathrm{red}}^{2}$ used to cluster QSO spectra excludes pixels in the Lyα forest. Above z = 2.6, the Lyα forest is present in an increasingly significant portion of the spectrum. For this reason, QSOs at 2.6 < z < 5.0 have been excluded from the first stage of clustering. We retrieve these high-redshift spectra by adding them to the existing clusters of the 2.4 < z < 2.6 bin in a similar fashion to the outliers.

We first divide the z > 2.6 spectra on the median S/N of the 2.4 < z < 2.6 redshift bin. The ${\chi }_{\mathrm{red}}^{2}$ is calculated between pairs of the z > 2.6 spectra and cluster representative spectra in the S/N bin corresponding to the high-redshift spectrum's S/N. The distance metric is determined in the overlapping wavelength range of the pair, restricting the comparison to 1216 Å < λ_RF < 2884 Å. A high-redshift spectrum is then added to all clusters for which the ${\chi }_{\mathrm{red}}^{2}$ to the representative spectrum is less than 150% of the initial distance threshold of that bin.

An error-weighted mean composite spectrum is then computed from all clusters as follows. The processed spectra (Section 2.1) belonging to clusters from the z < 1.3 subsample are normalized over 3620–4510 Å in the RF. The processed spectra belonging to clusters from the 1.0 < z < 5.0 subsample, excluding z > 2.4, are normalized over 1815–2880 Å. A different RF range of 1275–1725 Å is required to normalize the spectra in clusters at z > 2.4 owing to the extended wavelength coverage of the clusters.

All individual spectra are adjusted to the continuum slope of the representative spectrum using the c λ^Δα correction when taking the error-weighted mean of a cluster in the 1.0 < z < 5.0 subsample. The cluster composite spectra from the z < 1.3 subsample are simple error-weighted means. Thirty pixels on each extreme of a composite spectrum are removed to reduce edge noise. Lastly, we mask missing flux values and outlier pixels in each composite spectrum. Outlier pixels are identified identically as in the training sample, except if the threshold to be masked is 3σ positive or negative.

We reported a redshift-dependent bias on Z_PCA in BD22. We showed the bias could be stabilized by eigenspectra trained in the RF of the Mg ii emission line (see BD22 Figure 9). The use of Mg ii as a stable redshift estimator is similarly reported by Hewett & Wild (2010). We therefore shift all composite spectra so that the Mg ii line is at the expected RF wavelength using an improved version of the redshift correction method in BD22 (see Section 3.3 of BD22). This correction is enabled by the high S/N of the composite spectra, which facilitates a direct fit to the line location.

We approximate the underlying flux that is not associated with Mg ii emission by fitting a power law over 2600–2725 Å and 2875–2950 Å. After subtracting the power-law fit, a double Gaussian is fit to 2730–2870 Å. We impose a lower bound on the dispersion of 250 km s⁻¹ for both components of the Gaussian and require the two peak positions to be identical. The continuum and line profile are fit twice with pixels that deviate by more than 3σ from the first fit masked in the second. The iterative fitting reduces the influence of associated absorption features on estimating the line location. The wavelength solution of the spectrum is then shifted so the line center is at the RF wavelength of 2798.75 Å (consistent with Vanden Berk et al. 2001). This method for fitting the continuum and line profile neglects Fe ii emission (e.g., Wills et al. 1980, 1985; Vestergaard & Wilkes 2001), which can impact the measured line widths. Since we are only concerned with determining the line center, we do not include an iron template and rely on the continuum estimate to absorb iron contributions. Systematic offsets on our Mg ii location estimate will contribute to redshift errors in the final QSO templates for DESI. We explore the magnitude of systematic redshift offsets in Section 4.2.2.

Cluster composite spectra of the 10,905 clusters from z > 0.35 redshift–S/N subbins (Table 2) are corrected with this method. The procedure fails to fit the Mg ii emission line in 134 cases. VI of these spectra reveals clear contamination from stellar spectra or redshift errors in most cases. We reject these composite spectra and their contributing spectra from the further analyses.

The Mg ii emission line falls off the blue end of (e)BOSS spectra at z ≤ 0.35. It therefore cannot be used to correct for potential redshift offsets in the composite spectra of z < 0.35 clusters. We use a different approach to place these composite spectra in the same frame as the others. We apply a weighted expectation maximization principal component analysis (EMPCA; ³⁸ Bailey 2012) to the mean-subtracted reredshifted cluster composite spectra of the z < 1.3 subsample. EMPCA was designed to determine eigenvectors of data sets with noise or gaps, using measurement uncertainties to weight the input data. The composite spectra are median normalized over their common wavelength coverage and weighted by their propagated inverse variance. We then fit the mean spectrum plus the first five eigenspectra from EMPCA to the composite spectra of the z < 0.35 clusters. We fit only 3100–7000 Å by the current RF solution to ensure coverage by the eigenspectra. Each spectrum is fit at intervals of 69 km s⁻¹, the resolution of (e)BOSS spectra, over ±2070 km s⁻¹ and then shifted to the new redshift solution.

As shown in Figure 2, larger redshift corrections are required with increasing redshift and the corrections tend more red (Z_PCA is underestimated relative to the Mg ii RF). The trend is possibly driven by the blueshifting of high-ionization lines, such as C iv and Lyα, with respect to Mg ii, a less biased line. The greater flux density of these lines relative to Mg ii tends to dominate the fit during redshift estimation. Further, the Lyα forest is present in spectra at z > 1.92, a clear inflection point in this figure.

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After redshift corrections, we subtract the error-weighted mean of cluster composite spectra of the z < 1.3 subsample from all composite spectra within that subsample. We then derive eigenspectra from the residuals using EMPCA. We weight the flux values by the propagated inverse variance. This results in a model consisting of a mean vector and the first five eigenspectra from EMPCA that covers approximately 1800–9600 Å in the RF. We repeat these steps with the cluster composite spectra from the 1.0 < z < 5.0 subsample, creating a second spectral model with different RF wavelength coverage of approximately 600–5200 Å. The high-redshift model is padded with an exponential decay out to λ_RF = 590 Å to provide redshift coverage up to z = 5.05.

New to BD22, these eigenspectra do not comprise our final QSO templates. There are two main issues with using the composite-derived templates for classification in DESI. First, all the spectra within a cluster have individual redshift errors. Although small, the varying redshift offsets within a cluster lead to blurring and peak dampening of the emission lines in the composite spectrum. These features may negatively affect modeling. Second, the clusters overlap in membership with one spectrum potentially belonging to tens of clusters. The cluster overlap is desirable to avoid harsh boundaries on smooth population gradients, but, if we use eigenspectra from the cluster composites as the QSO templates, we introduce an artificial up-weighting of more common spectral features.

We instead use Redrock with the high- and low-redshift QSO models derived from the composite spectra to fit the calibrated spectra of the training sample and derive new redshifts. We mask pixels in the Z_PCA RF at λ_RF < 1216 Å while fitting. Additionally, if the spectrum has a nonzero BAL_PROB attribute indicating BALs are present (Guo & Martini 2019), we mask pixels in the following Z_PCA RF ranges: 1479–1549 Å, 1326–1397 Å, and 1216–1240 Å. These ranges correspond to the typical wavelengths of C iv, Si iv, and N v BALs. Lastly, we also remove pixels at λ_obs > 9700 Å owing to a lack of coverage from the low-redshift templates as they approach z ≈ 0.05. This reredshifting step aims to reduce the redshift bias seen in Figure 2 while addressing the issues outlined in the previous paragraph.

In the overlap redshift range of the models, we observe strong agreement in the redshift estimates from the two eigenspectra sets. For these spectra, we use the redshift from the model that provided the lowest ${\chi }_{\mathrm{red}}^{2}$ fit. We reject spectra from the final training sample that have a nonzero ZWARN attribute or ∣Δz∣ > 0.05 between the new redshift and Z_PCA. This cut effectively removes all the outlier spectra that exhibit calibration errors, incorrect classifications, or little signal and leaves most true QSO systems in the final sample except those displaying extreme peculiarities. We refine the redshifts of spectra with a new redshift of z > 1.92 by updating the Lyα forest mask and refitting over ±5000 km s⁻¹ from the initial redshift estimate. On average, the initial redshift estimate with these templates is redder than Z_PCA and the refined redshifts are almost always redder than the initial redshift. Our final model is trained using these new redshifts.

We suggested in BD22 that using multiple QSO template sets, each trained to reconstruct the variation observed over limited redshift intervals, should improve spectral modeling over the full QSO population (supported by Yip et al. 2004). Toward this goal, we create two QSO eigenspectra sets that together serve as the QSO templates for spectral classification in DESI. The new DESI QSO templates consist of a low-redshift eigenspectra set and a high-redshift eigenspectra set. The sets are trained on subsamples of the individual spectra of the reredshifted, pruned training sample introduced in the previous subsection. The templates are derived with EMPCA, weighting flux values by their inverse variance.

We tested several redshift boundaries when defining the training subsamples for the high- and low-redshift QSO eigenspectra. The maximum redshift for the low-redshift training sample varied between z = 1.4 to z = 1.9 while the minimum redshift for the high-redshift training sample varied between z = 1.0 to z = 1.5. The two training samples always overlapped in redshift by Δz = 0.4 to allow a smooth transition from one set to the next when classifying DESI spectra with Redrock.

All high-redshift templates are padded with a fast exponential decay beyond λ ≈ 600 Å to extend the redshift coverage to z = 7.0. Though the QSO number density is low beyond z ≈ 4.5 as seen by DESI, the padding ensures coverage for classifying the highest-redshift observations. The choice of exponential decay is so that the flux at these wavelengths is close to zero, as expected beyond the Lyman break, while avoiding zeros and discontinuities. A single template set that was trained on all redshifts, analogous to the previous DESI QSO templates, was also created for comparison.

In all cases, the templates consisted of the mean spectrum of its training sample plus the first N eigenspectra from EMPCA on the residual spectra. N was varied for each template option to determine how many eigenspectra were necessary to achieve high-accuracy QSO classification on the DESI Truth Table without introducing problems in the galaxy sample from overflexibility. We evaluated the accuracy, completeness, and catastrophic failure rates of classifications with Redrock on the DESI Truth Table (similar to Section 4.1) as well as the quality of the fits to determine the optimal choice for classification in DESI. The full redshift range template set underperformed relative to all high- and low-redshift template combinations evaluated in this work for all N tested.

We find that a mean plus three eigenspectra model in which the low-redshift set, trained on z < 1.7 spectra, classifies QSOs over 0.05 < z < 1.6 and the high-redshift set, trained on z > 1.3 spectra, classifies QSOs over 1.4 < z < 7.0 performs the best. This choice of redshift boundaries outperformed other models by ∼5%–10% in terms of completeness. Including higher-order eigenspectra marginally improves completeness but at the expense of reduced galaxy sample completeness and quasar sample purity below z = 1.5. The redshift range for classification differs from training due to the differences in wavelength coverage between SDSS and DESI and template binning in Redrock. We report only the results from the best-performing templates in Section 4, omitting the performance of the alternative options for brevity.

The new QSO template sets are shown in Figure 3 along with previous DESI QSO templates for comparison. Spectrophotometric calibration is degraded at the shortest observer-frame wavelengths in SDSS spectra (see Margala et al. 2016). As such, both the previous and high-redshift QSO templates suffer from reduced modeling power at the shortest wavelengths, namely beyond the Lyman limit, where SDSS QSO numbers are sparse. On the red side of the Lyman limit, the most notable difference from the previous to the current templates is an overall reduction of random noise attributed to the increased training sample size.

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Figure 3 also highlights the improvement of using template sets specialized for specific redshift intervals. The high-redshift set is overall similar to the previous templates, but there is a marked difference at low redshift. Particularly, the spectra lack the unphysical break in continuum present in the previous templates near 4000 Å. This is likely a result of the greater flux density and high variance at shorter wavelengths dominating the previous templates and leading to unphysical continua at longer wavelengths to maintain orthogonality.

The VI labels in the DESI Truth Table and QSO Main samples include a spectral class and redshift, allowing us to estimate the contamination fraction, incompleteness, and catastrophic failure rates in the QSO samples from Redrock with the new QSO templates. We also review the Redrock galaxy sample from the DESI Truth Table for potential impacts from updating the QSO templates.

A contaminant in a sample is defined as a spectrum for which the VI and Redrock spectral classes disagree or the Redrock redshift is bad. A good Redrock redshift for a QSO spectrum requires that

$$\begin{eqnarray}&&| {\rm{\Delta }}v| =\displaystyle \frac{| {z}_{{VI}}-{z}_{\mathrm{Redrock}}| }{1+{z}_{{VI}}}\times c\lt 3000\,\mathrm{km}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 1 }$$

We use a stricter definition of a good redshift for the galaxy sample, requiring ∣Δv∣ < 1000 km s⁻¹. The catastrophic failure rate is a subset of the contamination fraction, isolating only bad Redrock redshifts regardless of spectral-class correctness. The incompleteness of each sample is the number of spectra with VI spectral class of QSO (galaxy) that is not included in the Redrock QSO (galaxy) sample.

The contamination fraction, catastrophic failure rate, and incompleteness for the Redrock QSO and galaxy samples from the DESI Truth Table and the Redrock QSO sample from QSO Main are reported in Table 3. The same metrics for the previous QSO templates are also included in the table. Overall, both QSO samples show clear improvement with the change of templates while the galaxy sample exhibits minimal change. Assuming a binomial distribution, the new QSO templates lower the incompleteness of the QSO Main sample by 32% ± 3% and reduce the catastrophic failure rate by 50% ± 11%. A similar gain in completeness is achieved for the broader QSO sample as well, with a reduction in catastrophic failures of 32% ± 8%

Figure 4 shows the contamination fraction and incompleteness with redshift for the three samples. With the new templates, Redrock achieves a more complete QSO sample on the DESI Truth Table and QSO Main at all redshifts z > 0.5. This is reflected by the reduced contamination in the galaxy sample, indicating some QSOs previously misclassified as galaxies are now being placed in the correct sample. At all redshifts, the new QSO templates reduce the contamination in the QSO sample from QSO Main while achieving a lower or comparable contamination fraction in the QSO sample from the DESI Truth Table.

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There are 132 objects in the DESI Truth Table that are classified as QSO by Redrock with the new QSO templates and were not classified as QSO with the previous templates. Figure 5 shows a representative selection of these spectra, illustrating the types of QSO recovered. Many of the new Redrock QSOs display dust-reddened continua or strong absorption features that likely contributed to misclassification under the previous templates. A known issue with the previous templates is missing narrow or weak Mg ii emission, necessitating the Mg ii QSO afterburner (Alexander et al. 2023; Chaussidon et al. 2023). The new templates recover many of these as Redrock QSOs, though the afterburner is still necessary to reach the desired QSO completeness.

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Figure 5 also highlights a failure mode of Redrock generally. A small number of high-redshift Lyα emitter (LAE) galaxies are inadvertently targeted as QSO or galaxy. These systems are not classifiable as galaxy at the correct redshift with Redrock owing to the range of the galaxy templates (0 < z < 1.7). As a result, many of these objects appear in the QSO sample, with the Lyα line flux fit by the QSO template Lyα. The redshifts of true LAEs classified as QSO are only approximate since Lyα emission is broad in a QSO spectrum. Future work in DESI may explore an intentional LAE target class with a devoted template set for classification and redshift fitting.

4.1.1. Classification Accuracy and Completeness from Redrock with QSO Afterburners

4.1.2. Average Spectral Properties of Redrock QSOs

The median composite of spectra in the DESI Truth Table classified as QSO by Redrock with the new QSO templates is shown in the top panel of Figure 6. Also shown is the median composite of QSO spectra that were missed by Redrock but recovered by the QSO afterburners. This figure does not fully convey the diversity of Redrock and missed QSOs but illustrates the average spectral properties seen in a typical Redrock QSO spectrum while providing insight into the type of spectral features that the new QSO templates struggle to reconstruct.

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The bottom panel of Figure 6 shows similarly constructed composite spectra for the previous QSO templates, originally presented by Alexander et al. (2023). The missed QSO composite is constructed from a larger sample than with the new QSO templates, as their study focused on afterburner performance.

The typical spectrum classified as QSO by Redrock with the new QSO templates differs most from the typical missed QSO spectrum at λ_RF < 3700 Å where their underlying continua diverge. The QSOs missed by the new QSO templates tend to display more reddened continua in this range, similar to those missed by the previous QSO templates. For both template sets, a typical missed QSO may also display stronger host galaxy features such as the Balmer series and Ca H + K stellar absorption lines observed over 3700–4000 Å as well as increased [O ii] and [O iii] flux. While the afterburners recover many of the QSO spectra that Redrock missed, a few percent of QSOs are still missed entirely (Table 4). Often, these QSOs have low S/N, very red continua, or strong absorption features.

Table 4. Results from VI of Spectra in Guadalupe That Have Discrepant Redrock-only Classifications between the Previous and New QSO Templates

Target	Discrepancy	Total	New Templates	Previous Templates	Neither	Low
Type		Inspected	Correct	Correct	Correct	Quality
QSO	Redshift	100	70	16	5	9
	Spectral Class	100	70	8	12	10
ELG	Redshift	100	48	9	20	23
	Spectral Class	100	61	9	5	25
LRG	Redshift	90	28	9	28	25
	Spectral Class	100	59	0	33	8
BGS	Redshift	48	13	4	14	17
	Spectral Class	100	72	1	24	3

Note. We select two samples from each target type: redshift discrepant and spectral-class discrepant. Spectra in a given sample may exhibit both types of discrepancies however. Low Quality indicates spectra that could not be confidently classified through VI.

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A notable difference in the missed QSO spectra from changing the QSO templates appears in the equivalent width of broad lines such as C iv, C iii], and Mg ii. The equivalent widths of these lines in the typical missed QSO are smaller with the new QSO templates than with the previous QSO templates. This change indicates the new templates can describe more of the line profile parameter space, typically missing only the most narrow of broad line systems.

4.1.3. Classification Discrepancies Between the Previous and New QSO Templates

As a last step in evaluating the catastrophic failures, completeness, and contamination, we visually inspect spectra in Guadalupe that have discrepant Redrock-only classifications between the previous and new QSO templates. Classification discrepancies occur when Redrock assigns a different spectral class (galaxy, QSO, or star) or redshift to the same spectrum depending on the QSO templates used. The threshold for a redshift to be considered discrepant is defined as

$$\begin{eqnarray}&&| {\rm{\Delta }}v| =\displaystyle \frac{| {z}_{\mathrm{previous}}-{z}_{\mathrm{new}}| }{1+{z}_{\mathrm{previous}}}\times c\gt 3000\,\mathrm{km}\,{{\rm{s}}}^{-1}.\end{eqnarray} \tag{ 2 }$$

The breakdown of classification discrepancies by target type is shown in Table 5.

Table 5. Occurrences of Classification Discrepancies between the Previous and New QSO Templates by Target Type in the Guadalupe Sample

Target Type	QSO	ELG	LRG	BGS
Total Targets	435,538	498,367	404,361	1,149,884
Spectral Class	21,911	8,623	7184	7704
Redshift	23,009	7037	1448	695
Both	13,326	4394	1254	497

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VI is a time-consuming task and inspecting all spectra in Guadalupe that change classification is infeasible. Instead, we VI only a subset of spectra from Table 5 to estimate the consequences of the changed classifications. We choose 100 spectra that are discrepant in spectral class and 100 that have discrepant redshifts randomly from each target class over 40 tiles. Exclusivity is not enforced between the samples of discrepant spectra within a target type. Only 48 and 90 spectra have redshift disagreements over the selected tiles for BGS and LRG targets, respectively. This leaves a final selection of 738 spectra for VI.

Each spectrum in our VI sample was assigned to four inspectors who evaluated it using Prospect. ³⁹ Prospect is a VI tool developed for evaluating DESI's pipeline performance and target selection methods in the early survey. In short, Prospect displays an observed spectrum that can be interactively smoothed by the inspector. The top nine best template fits from Redrock can be overlaid on the spectrum for reference. Properties associated with each fit are also available in the VI tool, including the χ², redshift, and spectral class (see Lan et al. 2023 for detailed descriptions of Prospect). Each inspector indicates a spectral class and redshift of the spectrum along with the confidence of their assessment on a scale of 0 to 4. A confidence of 0 indicates no signal, 1 indicates there is one strong spectral feature present with a probable identification, 2 indicates more than one spectral feature has been identified, but features may be weak, and 4 indicates two or more spectral features are securely identified. An average confidence of 2.5 is the minimum value to be considered a confident classification.

The VI results of the four inspectors inform a final classification "truth" table for the sample. Special attention is given to resolving the classifications of spectra for which the inspectors disagree. We use only confident VI classifications in our analysis, reporting the remainder as "Low Quality."

The classification under a given QSO template set is considered correct if (1) the Redrock spectral class agrees with the VI spectral class and (2) the Redrock redshift is less than 3000 km s⁻¹ from the VI redshift for QSO targets or less than 1000 km s⁻¹ from the VI redshift for galaxy targets. A few instances exist where both template sets satisfy these criteria on a given spectrum. For these cases, the template set that provides the redshift estimate closest to the VI redshift is labeled as correct. Discrepant classifications for which neither template set satisfies both criteria are reported under "Neither Correct." The results from VI of the discrepant spectra are summarized in Table 4, broken down by target type and type of discrepancy.

The confident VI classifications of both spectral-class- and redshift-discrepant spectra indicate an improvement with the new QSO templates for all target types. Redshift-discrepant spectra with an LRG or BGS target type, however, have a high occurrence rate of neither template set achieving the correct classification. In most cases, the failure stems from problematic reductions of the spectra, such as discontinuities in flux, that impact the template-fitting ability rather than a problem with the QSO templates themselves.

This subsection is devoted to the redshift performance of the final classifications (Redrock with QSO afterburners) with the new QSO templates. We present estimates of the redshift precision, the catastrophic failure rate, and average redshift bias. We also briefly discuss the redshift performance specific to BALQSOs.

4.2.1. Redshift Precision Measured by Repeat Exposures

The multiple spectra for QSO targets in the SV Repeat Exposures sample can be used to determine a lower bound on the redshift precision and estimate the catastrophic failure rate at the main survey depth. We measure the precision as the dispersion of the velocity offsets between pairs of repeat exposures. The dispersion is calculated using the median absolute standard deviation (MAD) scaled by $1.4828\times {2}^{-\tfrac{1}{2}}$, following Alexander et al. (2023) and Lan et al. (2023). The catastrophic failure rate is defined as the percentage of these pairs with an absolute velocity offset, scaled by ${2}^{-\tfrac{1}{2}}$ to account for the measurement error on each redshift, over the typical failure threshold for QSOs of 3000 km s⁻¹ and a stricter threshold of 1000 km s⁻¹.

The measure of precision from repeat exposures provides only a lower-bound estimate on the true precision of QSO redshift estimates owing to the complex dynamics of QSO spectral features. Emission lines are often shifted nonuniformly from the systemic redshift, impacting the ability of a template-fitting software to extract the systemic redshift. Line dynamics that impact the redshift estimate obtained by the QSO templates will impact the redshift estimate in every exposure. The scaled MAD effectively estimates consistency or statistical precision.

The evolution of the scaled MAD with redshift is shown in Figure 7 for both the new and previous QSO templates along with their corresponding catastrophic failure rates. Redshift estimates from both QSO template sets are less precise as redshift increases until turning over at z ≈ 1.75, also reported by Yu et al. (2023). The rise and fall of redshift precision between 1.35 ≲ z ≲ 2.5 may be due to the presence of both the Mg ii and C iv emission lines in the spectra. These lines have different expected velocity offsets from the systemic redshift, which could introduce additional errors.

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At the main survey depth, the new templates clearly improve the precision at all redshifts. The redshift precision improves from ${100}_{-2.4}^{+2.7}$ km s⁻¹ to ${57}_{-1.3}^{+1.5}$ km s⁻¹ globally. The precision of both template sets is well below the DESI scientific and survey requirement for random errors between individual QSO redshift estimates of 750 km s⁻¹ (Abareshi et al. 2022), even at the redshift where the uncertainty peaks. The new QSO templates do not appear to impact the catastrophic failure rate at the failure threshold of 3000 km s⁻¹. DESI scientific and survey requirements dictate that the rate of catastrophic failures exceeding 1000 km s⁻¹ shall be less than 5% for tracer QSOs. Using this failure threshold on the SV Repeat Exposures sample yields a catastrophic failure rate of 4.0% and 4.6% for the new and previous QSO templates, respectively, meeting the requirements in both cases.

4.2.2. Cross-correlation With Other Tracers

Bias and systematic uncertainty on QSO redshifts manifest in the characteristics of the small-scale peak of cross-correlation functions in the radial direction. The radial shift of the peak from zero, Δr_∣∣, quantifies the average bias of the QSO redshift estimates while the width of the peak, σ_v , is influenced by redshift precision (Font-Ribera et al. 2013; du Mas des Bourboux et al 2017; A. Bault et al. 2023, in preparation). An absolute value of QSO redshift precision cannot be determined from this measurement, however, as several cosmological parameters and nonlinear effects contribute to σ_v in addition to redshift errors. We instead use the relative σ_v between the correlation functions produced by the different QSO template sets with a given non-QSO tracer to quantify the change in QSO redshift precision from changing templates. We assume these distortions of the small-scale peak of the cross-correlation functions arise from the QSO redshift errors and not from the redshift errors on the other tracers. The physics of non-QSO tracer systems is better constrained, so we treat non-QSO redshifts as effectively error free relative to the QSO redshifts.

We calculate the two-point cross-correlation function between QSOs and galaxies in the One-Percent Survey and between QSOs and Lyα absorbers in Guadalupe using the pycorr ⁴⁰ software package and the picca ⁴¹ software package, respectively. All correlation functions are determined over radial separations of −40 < r_∣∣ < 40 Mpc h⁻¹ and integrated from 0 to 200 Mpc h⁻¹ in the transverse direction.

We determine the cross-correlation function between QSOs and LRGs over 0.8 < z < 1.1, QSOs and ELGs over 0.8 < z < 1.6, and QSOs with redshifts of 2.0 < z < 4.0 and Lyα absorbers along their sight lines. The Lyα–QSO cross-correlation function is fit jointly with the Lyα autocorrelation function to reduce parameter degeneracy. DESI ELG targets overlap with DESI QSO targets, so we require a "galaxy" classification for ELGs in these measurements. The ELG and Lyα cross-correlation measurements are split on redshift to check for any evolution in the bias and precision of the QSO redshifts.

Figure 8 shows an example of the small-scale signal we are measuring in the Lyα–QSO cross-correlation. The x-axis corresponds to ∣r_∣∣∣ ≲ 37 Mpc h⁻¹, converted to km s⁻¹ for interpretation as redshift errors. The amplitude of the small-scale peak is negative because Lyα is a negative bias tracer. The difference in peak width between the previous and new QSO templates seen in Figure 8 corresponds to the difference in QSO redshift precision. This change in precision is captured by the ratio of σ_v in Table 6. We determine the best-fit value for the radial shift of the small-scale peak, Δr_∣∣, and the corresponding peak width, σ_v , for each correlation function. The best-fit Δr_∣∣ values are given in Table 6 for each tracer population along with the ratio of σ_v between the correlation functions produced by the different QSO templates.

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Table 6. QSO Redshift Uncertainties Measured from Cross-correlations with LRGs, ELGs, and Lyα Absorbers

		Previous QSO Templates		New QSO Templates
Redshift Range	Data Set	zeff	Δr∣∣ (km s−1)	zeff	Δr∣∣ (km s−1)	σv,new/σv,prev
0.8 < z < 1.1	LRG × QSO	0.954	−75 ± 10	0.954	−3 ± 10	0.990 ± 0.038
0.8 < z < 1.1	ELG × QSO	0.961	−40 ± 11	0.961	31 ± 8	0.986 ± 0.046
1.1 < z < 1.6	ELG × QSO	1.353	−17 ± 8	1.352	59 ± 8	0.921 ± 0.035
2.0 < z < 2.5	Lyα × QSO	2.171	−132 ± 31	2.172	9±29	0.948 ± 0.307
2.5 < z < 4.0	Lyα × QSO	2.753	−236 ± 46	2.756	−84 ± 31	0.501 ± 0.152

Note. z_eff is the effective redshift of the correlation function, Δr_∣∣ characterizes the average bias of the QSO redshifts estimates, and σ_v captures the effects of several redshift uncertainties including redshift errors. A reduction of σ_v demonstrates an improvement in the combination of statistical and systematic errors on the redshift estimates when using the new QSO templates.

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Redshifts from the new QSO templates are significantly less biased in most correlations. Δr_∣∣ is consistent with zero at 68% confidence over two of the redshift ranges evaluated, a statement that is not true at any redshift with previous QSO templates. The exception to improvement in absolute bias comes from the ELG–QSO cross-correlation. The new QSO templates produce absolute biases consistent with the previous QSO templates over 0.8 < z < 1.1, but the biases over 1.1 < z < 1.6 increase as a result of the general 70 km s⁻¹ shift seen in all galaxy–QSO cross-correlations. This shift can likely be attributed to the slight difference in RF between the previous and new template sets (Section 3.2).

A large reduction in σ_v is observed at the highest redshifts, indicating greatly improved redshift precision. The value of σ_v decreases with the new QSO templates across all tracers at the other redshifts evaluated, indicating some improvement at z < 2.5 though to a lesser extent. The observed improvement in precision is consistent with the findings of Section 4.2.1.

4.2.3. Redshift Success for BALQSOs

The scientific and survey requirements for DESI as a Stage IV dark energy survey are detailed in Table 3 of Abareshi et al. (2022). Below, we map the performance of the new QSO templates to the relevant scientific and survey requirements for redshift success of tracer (z < 2.1) and Lyα (z > 2.1) QSOs.

L2.4.2, L2.5.2: the random redshift error shall be less than σ_v = 0.0025(1 + z), or equivalently 750 km s⁻¹ rms.

The MAD of velocity offsets between redshift pairs in the SV Repeat Exposures sample measures the statistical precision, or the random redshift error, of redshift estimates for QSO targets in DESI. As shown in Figure 7, the statistical redshift precision of the new QSO templates is less than 150 km s⁻¹ over 0.0 < z < 4.0 and drops below 50 km s⁻¹ for z < 1.25 and z > 2.75.

L2.4.3: systematic inaccuracy in the mean redshift of tracer QSOs shall be less than Δz = 0.0004(1 + z) or equivalently, 120 km s⁻¹ .

The average inaccuracy, or bias, of QSO redshifts is measured as Δr_∣∣ in the fit to cross-correlation functions with other DESI tracers (Section 4.2.2). We only measure the bias of tracer QSO redshifts over 0.8 < z < 1.6, defined by the overlap in redshift distributions with the other non-QSO tracers targeted by DESI. The maximum average inaccuracy in this range is 59 ± 10 km s⁻¹. Additionally, the average inaccuracy of Lyα QSO and BALQSO redshifts over 2.0 < z < 4.0 is less than 120 km s⁻¹ with the new templates, though no minimum redshift accuracy is specified for high redshifts.

L2.4.4: catastrophic failures exceeding 1000 km s⁻¹ shall be less than 5% for tracer QSOs.

The typical tracer QSO in DESI will receive an exposure equivalent to the main survey depth. Therefore, the projected catastrophic failure rate is adequately estimated by limiting the SV Repeat Exposures sample to z < 2.1. This yields a catastrophic failure rate of 3.9% for tracer QSOs at the 1000 km s⁻¹ threshold.

L2.5.3: catastrophic failures shall be less than 2% for Lyα QSOs.

Similar to above, a catastrophic failure rate for Lyα QSOs is estimated by limiting the SV Repeat Exposures sample to z > 2.1. The rate of catastrophic failures exceeding 1000 km s⁻¹ is 4.1% with the new QSO templates, compared to 5.6% with the previous QSO templates. The new QSO templates achieve a catastrophic failure rate of 1.7% if the failure threshold is relaxed to 3000 km s⁻¹, compared to 1.9% with the previous templates. Lyα QSOs, unlike tracer QSOs, will be observed at least four times to enhance the S/N of their spectra. As such, the catastrophic failure rates determined here may be an overestimate.